Linear Relationships Review

Front

What is the Point-Slope form of a linear equation?

Back

The Point-Slope form is given by the equation: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you convert an equation from Point-Slope form to Slope-Intercept form?

Back

To convert from Point-Slope form (y - y_1 = m(x - x_1)) to Slope-Intercept form (y = mx + b), solve for y.

Front

What is the Slope-Intercept form of a linear equation?

Back

The Slope-Intercept form is given by the equation: y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the formula to find the slope between two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).

Front

How do you determine the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is equal to the tangent of the angle (θ) that the line makes with the positive x-axis: m = tan(θ).

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.